March 6, 2001

1. WAVE MOTION: vibration (oscillation) of particles in a medium

A. the acoustic medium must contain particles that are elastic, that is, sloshy or springlike.

B. The motion of each particle sets adjacent particles in motion. Energy is transferred over distance by local motions of particles.

C. Types of waves: Differences in motion of particles with respect to motion of the wave front. All exhibit the same abstract properties.

1. Transverse. Particles move perpendicular to wave front. Like a wave in a rope or slinky.
2. Longitudinal. Particles move forward/backward re wave front. Like sound (or slinky).
3. Combination waves. Both horizontal and perpendicular motion. Like familiar surface waves on water.
4. Varying number of dimensions for the medium:

2. WAVE CYCLE AND GRAPH

A. Period (T) of a wave is duration between any point on a wave and the same point on the next cycle. Measured in milliseconds usually. T = 1/f. Notice there is as much negative portion as positive portion of thewave.

B. Frequency (f) is the number of cycles per second. f = 1/T. Often it is measured in thousands of Hz = kHz (at least in the auditory range).

C. Amplitude (A) of a wave, the instantaneous pressure or displacement of particles in the medium. The amplitude has no relation to wave speed or its frequency. A given sound with greater amplitude sound louder than the same sound with smaller amplitude.

D. Velocity of wave front motion (s) depends solely on the medium. Thus it is independent of A, T or f. Wave move at low velocity in a slinky but faster in air and faster still in water and steel.

3. Sound is wave motion, typically of air, in the (humanly audible) frequency range of 20 Hz--20 kHz. This figure of a piano keyboard shows at least the range of musical sounds. You can see that the musical scale is logarithmic and that the highest note on a piano is about 4kHz (still over 2 octaves below the highest frequency we can hear). The lowest note comes close the lower limit of hearing (at 27.5 Hz).

4. WAVEFRONT MOTION

A. Propagation - waves keep on going once initiated. However, in 2D or 3D media, their amplitudes get smaller over time since the energy gets spread over greater and greater distances.

B. Diffraction - waves bend around corners. Low frequencies bend better than high frequencies.

C. Reflection - waves reflect partially when resistance of medium increases

D. Additivity (or superposition). When several waves are in the same place at the same time, they just add to each other. Since (+4) plus a (-4) = 0, it is possible for two sounds to add up to no sound at all!

5. SOME WAVE TYPES

A. Pure tone or `simple sound.' The wave looks like a `sinusoid'. See the second figure above.

B. Complex waves: sum of two or more sinusoids, usually harmonically related (that is, integer multiples of a `fundamental frequency', the f0).
1. harmonic sounds: sound like a hum or buzz, `tones'
2. nonperiodic sounds: eg, nonharmonic tones (eg, bell) and noise (hiss or whoosh)
3. fundamental frequency - the lowest frequency component of a complex wave.

C. Fourier's Theorem: "Any wave that is periodic can be represented as the sum of sinusoidal components whose frequencies are integer multiples of the fundamental period with appropriately chosen amplitudes. "

D. Spectrum Display: a graph showing the sinusoidal components that are summed to equal some sound wave.

6. SOUND SPECTRA and ANALYSIS FILTERS

A. Filters. Since sound is always a sum of independent frequency components, specific frequencies can be added to OR subtracted from any sound. Various mechanical and electronic devices, called acoustic filters, can strengthen or weaken selected frequencies relative to other frequencies. Many things can be acoustic filters, for example, a physical tube, a room, a loudspeaker, a microphone, etc.

B. A Sound Spectrogram is a graphic display of the sinusoidal components of a sound. These displays are very useful

For more on speech spectra, check Port's speech acoustics page and the speech web references on the syllabus page.